Superresolution in periodic data storage media

ABSTRACT

This invention provides a method of acquisition of binary information that has been stored physically in a periodic storage medium. The method, referred to as matrix-method deconvolution (MMD), is useful for use with optical storage media using an optical addressing system that reads and writes binary information in a periodic array of nano-particles. With this MMD method, the density of existing memory systems can be boosted to between 10 and 100 Terabytes of data per cubic centimeter. This matrix-method deconvolution method compensates for the effects of the optical addressing system&#39;s point spread function. Prior knowledge of a system&#39;s point spread function and inter memory-center spacing is used.

CROSS REFERENCE TO RELATED U.S. PATENT APPLICATION

This patent application relates to U.S. provisional patent applicationSer. No. 60/258,302 filed on Dec. 28, 2000, entitled SUPERRESOLUTION INPERIODIC OPTICAL DATA STORAGE.

FIELD OF THE INVENTION

This invention relates generally to the storage and acquisition ofbinary information that has been stored physically.

BACKGROUND OF THE INVENTION

The speed, capacity, and usage of computers have been growing rapidlyfor several decades. With the development of multimedia and digitalcommunications, the quantity of data being processed has grown fasterthan the technology that supports it. These factors have given rise to acritical need for new modalities of high density memory. For example,data bases at major international laboratories such as CERN and medicalcenters are approaching requirements of petabit storage levels per year.Digital media will soon require terabit formats, (see S. Esener and M.Kryder, WTEC Panel Report 7 (1999) 5.2). It may well be that limitationsin storing and retrieving data may ultimately limit progress in this keysector to science and technology.

Recently the inventors have investigated the unique properties of apolymer photonic crystal with respect to applications as a medium forhigh-density 3-D optical data storage for this expressed purpose, see B.Siwick, O. Kalinina, E Kumacheva, R. J. D Miller and J. Noolandi, Appl.Phys. 90 (2001) 5328. This new class of materials has the uniqueproperty that information can be confined in spatially modulated domainswith well-defined Fourier components. The spatial order imposed on thedata storage process is achieved by using nanocomposite polymers inwhich the optically active domains are localized in the center ofself-assemblying latex particles through a two step (or multi-step)growth cycle. Core particles are formed by an optically activedye-labeled monomer. The cores are then subjected to a second stage ofpolymerization with a lower glass temperature that serves as theoptically inactive outer buffer. The resulting particles show very gooduniformity and are essentially monodispersed with respect to radii. Thisproperty facilitates the formation of hexagonally close packed films upto mm thickness with a very high degree of order. Upon annealing, theclose-packed core-shell particles form a nanostructured material withthe fluorescent particles periodically embedded into the optically inertmatrix in a close-packed hexagonal structure, see E. Kumacheva, O.Kalinina, L. Lilge, Adv. Mater. 11 (1999) 231. The long range periodicorder of these materials is demonstrated in FIGS. 1 a), 1 b) and 1 c).

To store information in these materials, a two-photon laser scanningmicroscope was used to write information by photobleaching the opticallyactive cores and, under much lower fluence, read out the resultingimage. The optical properties of these nanocomposite polymers areessentially binary in nature, i.e., the optically active domains areseparated by inactive regions with a square modulated cross sectiondetermined by the abrupt interface between the high and low temperaturepolymer blends. This binary modulation of the polymer's opticallyproperties makes these materials ideal for storing binary information,as can be appreciated from FIGS. 1 a), 1 b) and 1 c). The bleaching ofthe dye in the well defined spatial domains serves as part of the binarycode. The sharp boundaries and high local concentration of fluorescentdye serves to enhance the contrast and readily define the bit storage.Equally important, the writing speeds can support GHz address speeds.Overall, a storage density approaching 1 Terabit/cc was successfullydemonstrated as disclosed in B. Siwick, O. Kalinina, E Kumacheva, R. J.D Miller and J. Noolandi, Appl. Phys. 90 (2001) 5328.

Relative to conventional homogeneous storage media, the nanostructuredperiodic material is shown to increase the effective optical storagedensity by spatially localizing the optically active region and imposingan optically inactive barrier to cross-talk between bits. The basicprinciple that provides this unique property is shown schematically inFIG. 2. This feature alone leads to a significant increase in thestorage density of nanocomposite polymers relative to homogeneouspolymers, (B. Siwick, O. Kalinina, E Kumacheva, R. J. D Miller and J.Noolandi, Appl. Phys. 90 (2001) 5328). The aim of the current work is toexplore the possibility of further taking advantage of the periodicspatial properties of these materials.

Conventional limits in optical resolution (Rayleigh criterion) assume noa priori knowledge of the location of an object(s). In the case ofperiodic materials, the objects of interest are confined to latticepoints with a well-defined lattice spacing such that there is additionalinformation available for signal processing. The periodic nature of thesignal that would result from such structures is well suited to spatialphase sensitive detection methods, i.e. the underlying lattice periodacts as a reference for signal processing. Signal-to-noise enhancementsof several orders of magnitude are typically realized in relatedproblems using optical heterodyne detection. The question is how farcould the spatial resolution be improved by explicitly taking advantageof the underlying Fourier spatial components to nanocomposite materials.To this end, a post processing algorithm was developed that is optimalfor extracting binary information from images of bit patterns innanocomposite materials at densities far beyond the classic Rayleighresolution limit. Under realistic noise conditions, this signalprocessing procedure should lead to a density increase of an order ofmagnitude.

The storage density limit in optical systems is determined by theresolution of the imaging system. When observed through an opticalinstrument such as a microscope, the image of an individual bit appearsas an intensity distribution. The width of this distribution ordiffraction pattern is proportional to the wavelength λ of the light inthe imaging system. If the bits are separated by a distance λ, thenthere will be little interference between the diffraction patterns ofthe bits. We will refer to this spacing as normal density. As the bitseparation is reduced, it becomes harder to distinguish individual bits.When the central maximum of one bit's image falls on the first minimumof a second bit, the images are said to be just resolved. This limitingcondition of resolution is known as Rayleigh's criterion. In otherwords, if the distance between bits is smaller than λ/2 the microscopewill not be able to distinguish between two adjacent bits. We will referto this spacing as the classical limit density.

A CD-ROM that holds a maximum of 650 Mbytes over an area of 50 cm²(radius 4 cm) has a density of 13 Mbytes/cm². For such systems which usea 780 nm (infrared) laser the normal density is around 20 Mbytes/cm².Hence, commercial CD-ROMs operate at about 60% of the normal density.The bit density of a DVD that uses a 650 nm (red) laser is 7.8×10⁸bits/cm². For this wavelength the normal density is around 1.64×10⁸bits/cm², and the classical limit density, is 9.5×10⁸ bits/cm². Thecommercial DVD's operate near 80% of the classical limit density.Although the DVD's density is a great improvement (˜7 times more dataper disc) over the older CD-ROM technology, it is still limited bydiffraction as expressed in the Rayleigh criterion.

When two diffraction patterns are superimposed, in order to satisfy theRayleigh criterion, they must be separated by more than half the widthof the central peak. $\begin{matrix}{{r_{ij} > \frac{1.22\pi\quad z}{R\quad k_{0}}} = {{\frac{1.22z}{R}\left( \frac{\lambda_{0}}{2} \right)\quad{since}{\quad\quad}\lambda} = \frac{2\pi}{k}}} & \lbrack 1\rbrack\end{matrix}$where z is x, R is y, and λ₀ is z. The minimum resolved separationdistance (r_(ij)) is therefore proportional to half the wavelength. Thisrelation defines the maximum density that can be stored in the imageplane and is responsible for the λ⁻² scaling for 2-d optical storage. Bytaking advantage of confocal imaging to provide a 3^(rd) dimension, themaximum density scales as λ⁻³. The above relation then defines thestorage density for one page in the optical readout for 3-d memory andthe confocal parameter defines the density of these pages along theoptic axis. The density along the optic axis can be increased to acertain extent by using theta scans (see Steffen Lindek, Rainer Pick,Ernst H K Stelzer Rev. Sci. Instrum. 65, 3367 (1994)) however, thestorage density scales quadratically for in-plane components andprovides far greater gain in storage density.

It would be very advantageous to have a technique that allows data to beread at resolutions beyond the Rayleigh criterion.

SUMMARY OF THE INVENTION

Accordingly, one object of the present invention is to provide atechnique which allows data to be read from a periodic data storagemedia at resolutions beyond the Rayleigh criterion.

Another object of the present invention is to provide a method toresolve structures in images beyond the Rayleigh criterion, as well asto extract the binary information contained therein. Error Freedetermination of this information at bit densities exceeding theclassical limit would thus imply, an effective “super-resolution”.

For a periodic lattice memory system, the superresolution or MMD methoddisclosed herein is achieved by post-processing the images oftwo-dimensional pages of memory, either recorded simultaneously ortime-averaged (as with one-dimensional beam systems). Thispost-processing technique, described herein, is referred to asmatrix-method deconvolution, since it compensates for the effects of theimaging system's point spread function. Prior knowledge of a system'spoint spread function and interbit spacing is used. Also the centerco-ordinate of at least one bit must be determined to set the effectivephase of the spatially modulated signal.

The present invention provides a method of reading binary informationstored in a storage medium, comprising:

a) providing a storage medium having n memory-centers each with a knownposition and the memory-centers having substantially the same physicaldimensions;

b) accessing said storage medium with an addressing system and measuringfor each memory-center a scalar signal intensity I_(m) emitted from apre-selected region which is centered on the known position of saidmemory-center; and

c) extracting the stored binary information by calculating bit valuesb_(n) for all memory-centers using an equation B=C⁻¹ I/I_(o), whereinI_(o) is a predetermined normalizing factor, I=(I₁, I₂, . . . , I_(n))is an array of said scalar intensities for all memory-centers, andB=(b₁, b₂, . . . , b_(n)) is an array of bit values, and C is apredetermined cross-talk matrix of n² elements where each elementrepresents a cross-talk between said pre-selected regions.

In this aspect of the method, the value of each matrix element may bedefined as a function of a spacing between memory-centers i and j givenbyC _(ij) =f(r′)=f(| r _(i) −r _(j)|)=f(R _(ij))where f(r′) is defined as a cross-talk function, and wherein saidcross-talk matrix C is calculated by applying said cross-talk functionto each element of a matrix R that contains all inter-memory-centerspacings R_(ij)=r′=|r _(i)−r _(j)|.

In this aspect of the method the cross-talk function f(r′) may bederived from an intensity distribution within a preselected region I₀(q_(m)),${f\left( r^{\prime} \right)} = {{\oint{{\mathbb{d}\underset{\_}{q}}{I_{0}\left( {\underset{\_}{q}}_{i} \right)}}}\bigcap{I_{0}\left( {\underset{\_}{q}}_{j} \right)}}$where q_(m) defines coordinates of the intensity distribution of thepreselected region of the mth memory-center.

In this aspect of the invention a binary value for each memory-center iscalculated from a corresponding bit value by a process wherein the n₁highest bit values are assigned a binary value of ‘1’ and all others areassigned a binary value ‘0’ based upon an equation relating thepopulation of ‘1’ valued memory-centers,$n_{1} = {{\sum\limits_{j = 1}^{N}\quad\frac{I\quad j}{I_{0}}} = \frac{I_{N}^{total}}{I_{0}}}$

In another aspect of the invention there is provided a method of readingbinary information stored in a storage medium, comprising:

a) providing a storage medium having n memory-centers each with a knownposition and the memory-centers having substantially the same physicaldimensions;

b) accessing said storage medium with an addressing system and measuringfor each memory-center a scalar signal intensity I_(m) emitted from apre-selected region which is centered on the known position of saidmemory-center and having an intensity distribution defined by an impulseresponse of the addressing system and an effective distribution of thesignal stored within the addressed memory-center; and

c) extracting the stored binary information by calculating bit valuesb_(n) for all memory-centers using an equation B=C⁻¹ I/I_(o), whereinI_(o) is a predetermined normalizing factor, I=(I₁, I₂, . . . , I_(n))is an array of said scalar intensities for all memory-centers, andB=(b₁, b₂, . . . , b_(n)) is an array of bit values, and C is apredetermined cross-talk matrix of n² elements where each elementrepresents a cross-talk between said pre-selected regions.

The present invention also provides a method of reading binaryinformation stored in an optical storage medium, comprising:

a) providing an optical storage medium having n memory-centers each witha known position and the memory-centers having substantially the samephysical dimensions;

b) accessing said optical storage medium with an optical addressingsystem and measuring for each memory-center a total optical intensityI_(m) emitted from a pre-selected region which is centered on the knownposition of said memory-center and having an optical intensitydistribution within a single pre-selected region I₀(q) defined by apoint spread function of the optical addressing system and an intensitydistribution of the memory-center itself defined by an optical responseof a single memory-center as imaged through an idealized opticaladdressing system having an infinitely small point spread function; and

c) extracting the stored binary information by calculating bit valuesb_(n) for all memory-centers using an equation B=C⁻¹ I/I_(o), whereinI_(o) is a predetermined normalizing factor, I=(I₁, I₂, . . . , I_(m), .. . , I_(n)) is an array of said scalar intensities for allmemory-centers, and B=(b₁, b₂, . . . , b_(n)) is an array of bit values,and C is a predetermined cross-talk matrix of n² elements where eachelement represents a cross-talk between said pre-selected regions.

An advantage of the method of the present invention is that it removesthe data storage limit classically imposed by the Rayleigh criterionwith the only limit of data retrieval being related to noise conditionsrather than density.

BRIEF DESCRIPTION OF THE DRAWINGS

The method of the present invention will now be described, referencebeing had to the accompanying drawings, in which:

FIG. 1 a shows a structure of the addressed plane of a nanocompositememory storage medium located at the distance 200 microns from the topsurface, the scale bar is 5 microns and the particles have 500 nmdiameter cores and 250 nm thick shells;

FIG. 1 b) shows the structure of the addressed and adjacent layers ofthe nanocomposite storage medium of FIG. 1 a) studied by 2-photonconfocal microscopy;

FIG. 1 c) shows fluorescence intensity profiles for the addressed andneighboring planes of FIGS. 1 a) and 1 b);

FIG. 2 shows how a memory medium made of nanostructured materialssignificantly reduces the cross-talk in the writing and readingprocesses by spatial isolation/separation of the active memory centerscompared to homogenous memory storage materials;

FIG. 3 a shows the Regions of Interest (ROI) with no overlap betweenROI's

FIG. 3 b(i) shows the memory-centers or bits are close enough that ROI'soverlap a little, 3 b(ii) shows the resulting cross-talk between the ROIfrom the central ON bit;

FIG. 3 c(i) shows the memory centers close enough so there is highoverlap of the ROI's, 3 c(ii) shows the resulting cross-talk between theROIs in 3 c(i);

FIG. 4 a illustrates the definitions of r, the spacing between thememory centers or bits, and R, the radius of the diffraction pattern;

FIG. 4 b shows the basis vectors and the lattice translations for theperiodic storage memory where the dark circles represent the array ofperiodic memory centers;

FIG. 5 (top left) shows a laser confocal fluorescent microscopy image ofa nanocomposite particle array in which the memory centers have a corediameter 650±20 nm and shell thickness 200±5 nm. λ_(Fluorescnce)˜500 nm,λ_(two-photon)=844 nm, the resolution is approximately 256×256 samples,in which a data pattern has been photo-bleached into material (topright); after filtering and deconvolution approximate Gaussian pointspread function is shown in the bottom right, and at the bottom left asimulation of equivalent data with a sine squared basis bit is shownwith simulated point-spread function of diameter, 750 nm and signal tonoise ratio of 10;

FIGS. 6 a, 6 b, 6 c and 6 d show increasing overlap in random data atvarious densities;

FIG. 7 shows bit distributions, when the MMD method is applied tosimulated images the output values of the B_(n) vector tended to take ontwo distributions around 1 and 0; and

FIG. 8 shows plots of cross-talk % versus the signal to noise ratio foreither simulation show the regions in which the presen MMD method of thepresent invention can improve the resolving power of memory acquisitionsystems.

DETAILED DESCRIPTION OF THE INVENTION

A goal of the present method is not to resolve structures in the imagesbeyond the Rayleigh criterion, but rather to extract the binaryinformation contained therein. Error Free determination of thisinformation at bit densities exceeding the classical limit would thusimply, an effective “super-resolution”.

In the present method, for a periodic lattice memory system,superresolution is achieved by post-processing the images oftwo-dimensional pages of memory, either recorded simultaneously ortime-averaged (as with one-dimensional beam systems). Thispost-processing technique, described herein is referred to asmatrix-method deconvolution (MMD), since it compensates for the effectsof the imaging system's point spread function. Prior knowledge of asystem's point spread function and inter-bit spacing is needed. Also thecenter co-ordinate of at least one bit must be determined to set theeffective phase of the spatially modulated signal.

Matrix-Method Deconvolution (MMD)

We define the Region of Interest (ROI or pre-determined region) in animage of a bit to be that area encompassing the first (and mostsignificant) maximum of the bit pattern. FIG. 3 a shows the situation ofno overlap between ROI's, FIG. 3 b(i) shows memory centers being closeenough so that ROI's overlap a little and FIG. 3 b(ii) shows theresulting cross-talk between the ROI's from the central ON bit or memorycenter. FIG. 3 c(i) shows highly overlapping ROI's and FIG. 3 c(ii)shows the resulting cross-talk between the ROI's. Since this informationcan be reconstructed as a Fourier series of the lattice period, thepattern appears as an effective diffraction pattern to this periodicfunction and will be referred to as the bit diffraction pattern. Thetotal detected intensity I_(m) within the mth ROI ultimately determinesthe corresponding binary value. At densities in which there is anoverlap (cross-talk) between the ROI's, the total intensities I_(m) willincrease by an amount related to the proximity between bits, such that:$\begin{matrix}{I_{x} = {I_{0}{\sum\limits_{n}{c_{xn}B_{n}}}}} & \lbrack 2\rbrack\end{matrix}$where B_(N) is the binary value of the nth bit, I₀ is the maximumintensity within an isolated ROI and c_(xn)=c_(nx)=f(r_(n)−r_(x)) is thecross-talk coefficient.

If we include all of the bits in an array of N bits, we have a system ofN equations and N unknowns. $\quad\begin{matrix}\begin{matrix}{I_{1} = {I_{0} \times \left( {B_{1} + {c_{12}B_{2}} + {c_{13}B_{3}\quad\ldots} + {c_{1N}B_{N}}} \right)}} \\{I_{2} = {I_{0} \times \left( {{c_{12}B_{1}} + B_{2} + {c_{23}B_{3}\quad\ldots} + {c_{2N}B_{N}}} \right)}} \\{\vdots} \\{I_{N} = {I_{0} \times \left( {{c_{N\quad 1}B_{1}} + {c_{N\quad 2}B_{2}} + {c_{N\quad 3}B_{3}\quad\ldots} + B_{N}} \right)}}\end{matrix} & \lbrack 3\rbrack\end{matrix}$

In matrix form, these equations can be expressed asC _(nm) B _(m) =I _(n) /I ₀  [4]where C is an n×n matrix that shall be called the cross-talk matrix. Theoverlap leading to cross-talk between bits is shown schematically inFIG. 3.

To extract data from an image, we measure the intensities within eachROI, and calculate the bit values using the inverse of the previousequation:B _(m) =C _(nm) ⁻¹ I _(n) /I ₀  [5]C and I₀ are constant for a given combination of readout frequency andbit density, and can be calculated a priori if the function f (r_(lk))is applied to an array of inter-bit distances, r_(lk)=r_(l)−r_(k).Matrix Construction and the Cross-talk Function

The cross-talk function f(r_(lk)) is determined by the intensitydistribution I_(o)(x,y) of a bits image within its ROI, see FIG. 4 a,$\begin{matrix}{{f\left( r_{ij} \right)} = {4{\int_{r_{ij}/2}^{R}{\int_{0}^{y{(x)}}{{I_{0}\left( {x,y} \right)}\quad{\mathbb{d}y}\quad{\mathbb{d}x}}}}}} & \lbrack 6\rbrack\end{matrix}$or for discrete pixels $\begin{matrix}{{f(r)} = {4{\sum\limits_{r/2}^{R}\quad{\sum\limits_{0}^{y{(x)}}\quad{I_{0}\left( {x,y} \right)}}}}} & \lbrack 7\rbrack\end{matrix}$With higher resolutions, it was possible to approximate the cross-talkfunction f(r_(ij)) with a polynomial fit to speed up calculations, butfor lower resolutions the pixels make this smooth function very jagged,and instead, a look-up table was generated.

For each unique combination of bit size, spacing and point-spreadfunction, a different matrix has to be generated. Since there are N²components in C_(ij), the theoretical matrix construction is a secondorder algorithm. However, it can be reduced to an Nlog N order algorithmby taking advantage of the periodic lattice. To generate the cross-talkmatrix, an array was created for each bit containing the distancebetween it and the other bits; R_(ij)=|r_(ij)| is also an n×n matrix.Then the cross-talk function f(r_(ij)) was applied to each element of R.

The first row of R corresponds to the distances between the first bitand all others bit. This is calculated using integer combinations oflattice basis vector as shown schematically in FIG. 4 b,R _(1j) =A _(j) a+B _(j) b+C _(j) c.   [8]Then the jth row was calculated by transforming the origin from thefirst bit to the jth, i.e.,|R _(jk) |=|R _(1k) −R _(1j)|  [9]Once density specifications are chosen for a system, the cross-talkmatrix can be experimentally determined by recording the ROI intensitieswhen only one bit in the system is “on.”. The intensities measuredwithin all other ROI correspond to one row of the cross-over matrix. Allsubsequent rows are lattice vector translations of the first.

As stated above, the cross-talk matrix has N² elements. If N²instructions must be executed to access N bits, the speed of the memorysystem will be very slow. However, for values of N much larger than thenumber of overlapping diffraction patterns within a single ROI, theoverlap matrix will be very sparse. As the size of N increases thematrix becomes increasingly sparse and fewer calculations are necessaryto extract the information.

It should be noted that when memory is within the classical limitdensity, it is possible to extract the bits with a simple algorithm thatcompares the intensities of the ROI to a set threshold of say nI₀/2where n is the number of nearest neighbors. Yet even at these classicaldensities, there are advantages to using the MMD extraction procedure.It calculates each bit as a function of the intensities of thesurrounding bits, like a moving average/autogain algorithm, and furtherenhances the signal to noise as will be discussed below.

Simulation of Experimental Results

To simulate the two-photon confocal flourescence microscopy images ofdata stored in nano-structured polymer, we assumed a bit basis function:the first peak of a radially symmetric cosine squared function,$\begin{matrix}\begin{matrix}{{S\left( {x,y} \right)} = {{Cos}^{2}\left( {\frac{\pi}{2R}\sqrt{\left( {x - \frac{R}{2}} \right)^{2} + \left( {y - \frac{R}{2}} \right)^{2}}} \right)}} \\{{{{for}\quad\left( {x - \frac{R}{2}} \right)^{2}} + \left( {y - \frac{R}{2}} \right)^{2}} \leq R^{2}} \\{= {0\quad\text{(ignores~~second~~order~~maxima)}}} \\{{{{for}\quad\left( {x - \frac{R}{2}} \right)^{2}} + \left( {y - \frac{R}{2}} \right)^{2}} \geq R^{2}}\end{matrix} & \lbrack 10\rbrack\end{matrix}$This function was used as the basis to construct simulated close packedhexagonal lattices of random binary data and is shown in FIG. 5.Simulations were conducted by two different methods, to demonstratedifferent situations. In both methods, the diffraction of the bit basiswas calculated by convolving with an approximate Gaussian point-spreadfunction.I ₀(x,y)=I _(PSF)(x,y)*S(x,y)=∫∫I _(PSF)(x,y)S(x′−x,y′−y)dx′dy′where I_(PSF) is a spatial distribution of the impulse response andS(x,y) is the optical intensity distribution of the single memory-centeras measured through an idealized optical addressing system.Simulation A

The properties of the imaging system were held constant and theinformation storage density was varied. Hence, the radius of thediffraction pattern was kept constant and the bits were moved closertogether. The samples per unit area, the area of the ROI, and themagnitude of each diffraction pattern is held constant. When the profileof diffraction patterns are overlapping by 50% , the distance betweennearest neighbor bits is equal to half the diameter of the effectivediffraction pattern (λ/2), and it becomes difficult to visuallydistinguish nearest neighbor bits. This point is illustratedschematically in the series showing increasing overlap in FIGS. 6 a, 6b, 6 c and 6 d. This is the classical limit density. At 75%, thedistance between bits is a quarter the diameter of the diffractionpattern (λ/4). An image of the same quantity of data is now onesixteenth the size of the uncompressed lattice. This translates to a 3-ddensity improvement over normal density of 256 times.

Simulation B

The density of stored information was held constant and the propertiesof the imaging system (PSF) were varied. Alternatively this procedurecould be applied to a given imaging system, a given data density, byvarying the wavelengths of light λ₀. The distance between the bits isheld constant; while the width of the diffraction pattern is changed. Asthe point-spread function widens, the maximum intensity goes down. Whenthe radius of the diffraction pattern is equal to the spacing betweenthe bits, the effective cross-talk is 50%. This is the classical limitdensity for such a system, λ=2λ₀. At 75% effective cross-talk, λ=3λ₀,the diameter of the diffraction pattern is 3 times the distance betweenbits or, $\begin{matrix}{\text{Effective~~Cross-talk} = {{\left( {1 - {\lambda_{0}/\lambda}} \right)*100} = {\left( {1 - \frac{d_{core}}{2\quad G_{PSF}}} \right)*100}}} & \lbrack 11\rbrack\end{matrix}$where d_(core) is the core diameter and G_(PSF) is the FWHM of agaussian point spread function. It should be emphasized that for thissituation, an effective cross-talk of 100% requires an infinite pointspread function; whereas in the previous simulation, 100% cross-talkimplies that both bits were in the same location.

When the MMD was applied to simulated images the output values of theB_(n) vector tended to take on two distributions around 1 and 0, asshown in the bit distributions of FIG. 7 which is a series of MMD outputhistograms. As the noise was increased, the width of both ON and OFFpeaks in the histograms become wider, until a noise threshold wasreached, at which point the two bands of values begin to overalp and thealgorithm is no longer 100% accurate. Higher resolutions are affectedless by the noise because it is averaged whe nthe intensities Ij arecalculated from ROI with more bits contained within them. To extractinformation from the output, binary values must be assigned to each bit.Note that the population of 1's and 0's, is determined from the totalintensity within the image. $\begin{matrix}{n_{1} = {{\sum\limits_{j = 1}^{N}\quad{{I_{j}^{total}/I_{0}}\quad n_{2}}} = {N - n_{1}}}} & \lbrack 12\rbrack\end{matrix}$The n₁ highest valued bits are ‘1’ and the remaining n₂=N−n₁ bits areconsidered ‘0’.

The resolving power of the MMD method was tested in both situations byadding different kinds and levels of noise to the simulated images. Thesignal-to-noise ratio was defined as the ratio between the signal power(total intensity) and the noise power. The results summarized in Table 1were obtained by simulating arrays of 256 bits with each bit having adiameter of 16 pixels. These values were held constant throughout thesimulations, so as not to skew the results. The effects of changing thenumbers of pixels per bit disappear for large enough numbers of bits.The speed of the simulations was increased by choosing samplingparameters that were powers of two (allows an FFT algorithm to be used).

The noise threshold for error free determination of variousconfigurations of both simulation A and B were measured by slowlydecreasing the amount of noise until no errors were detected. Theregions of Error Free Signal (EFS) demonstrated with the MMD are shownin FIG. 8.

TABLE 1 Summary of Noise Threshold Results: 2D Density Improvement overEffective Threshold SNR [dB] normal Cross-talk White density [%] Noiseρ/ρ_(normal) Simulation A  0 −3  0 30 −3  2 50 −3  4 70 20 11 75 30.5 1690 46. 100  99.9 [∞] [∞] Simulation B  0 −3  0 30 −3  2 50 −3  4 67 −3 9 75 10 16 80 27.5 25 83 49 36 99.9 [∞] [∞]

The calculated improvements in information density are ratherremarkable. This potential increase in bit density that can be accessedthrough such a binary extraction method should be gauged relative toother approaches being explored. A great deal of technical effort ispresently being expended towards the development of blue diode lasers toincrease optical data storage by approximately a factor of two. Bysimply changing the material to a nanocomposite and using the MMDapproach it is possible to increase the density substantially beyondthis target. The effectiveness of this technique is due to the followingfactors; knowledge of the effects of the imaging system's point spreadfunctions, and the structure of the storage materials, i.e. the spatiallocation of each bit in the images.

It will be appreciated that the increase in data storage density isdetermined by the signal-to-noise in the read out. In particular, thewidth of the distributions in the algorithms output is related to theamount of noise in the image. This shows that the maximum resolvabilityof MMD will be dependent upon the system's signal-to-noise ratio, notthe diffraction limit defined solely by the optics. The noise effectsmay be reduced with spatial and temporal filters to further suppressbackground noise and to build in redundancy into an error correctionprocess.

There are several significant advantages of the matrix-methoddeconvolution (MMD) method disclosed herein. It can be exploited in anumber of different applications. It can be used to read out data atlonger wavelengths than the writing process. In order to writeinformation beyond the diffraction limit of the reading wavelengthrequires that the data be written at shorter wavelengths as this step isstill defined by diffraction limits of the optical imaging system. Thewriting process can be done with more expensive “blue lasers” to encodehigher density information and MMD enables the read out at longerwavelengths with more cost effective systems amenable to multiple users.The MMD method can be used for reading low density memory, in a systemthat has high noise levels. It can be used to read from storage mediasystems with limited sampling capability. The MMD is only dependant onthe total intensity within a ROI, hence the minimum sampling required isone sample per ROI. The matrix method of superresolution can work ineither one, two, or three dimensions, whether the pre-selected regionsof interest are lines, circles or spheres.

To summarize, a method has been disclosed hereinto achieve error-freeretrieval of binary information an order of magnitude beyond theRayleigh limit. The method disclosed herein to achieve substantiallyerror-free retrieval of binary information an order of magnitude beyondthe Rayleigh limit, known as the matrix-method doconvolution method(MMD), was tested on images that simulated an existing optical memorysystem. It was found that the MMD method successfully compensates forthe limitations of diffraction. Within current signal to noise limits indata read out, increases in optical density of more than 64 over theclassical density are achievable, without considering further signalconditioning and optimization.

The exploitation of the intrinsically periodic nature of nanocompositematerials gives memory storage media made of these nanocomposites anadvantage over homogeneous memory storage media in this regard.Notwithstanding, it will be understood that the present method can beused with homogenous or non nanocomposite media as well, although thebiggest improvement is expected using nanocomposite memory storagemedia.

The underlying period of the nanocomposite lattice provides an effectivespatial reference for signal processing and extracting additionalinformation. The combination of novel periodically photoactive materialsand image processing may provide the solution to our ever-increasingdemand for more memory at higher densities. Further, nanocompositematerials bring an extra dimension for optimizing the photoactiveprocesses for a variety of applications. By spatially varying theviscosity and polarity of the nanocomposite, it is possible to increasephotochemical quantum yields, create enhanced photo-electric indexmodulation, and minimize volume contraction in the recording process.All of these attributes can be further enhanced with respect toinformation density by explicitly exploiting the periodic nature ofthese materials, as illustrated with MMD approach for the simplestexample of binary code.

One type of nanocomposite material is the periodic array ofnano-particles being a polymer matrix comprising a three dimensionalarray of rigid polymeric cores embedded in a substantially transparentshell-forming polymer. each memory-center comprises a photosensitiveconstituent associated with each nano-particle. The photosensitiveconstituent may be chromophores on, within or otherwise associated withthe cores. More particularly the chromophores may be fluorescentmolecules. The information is stored optically within the memory-centersin the storage medium and the addressing is an optical addressingsystem.

While the method has been described in detail with respect to opticalstorage media and addressing systems, it will be appreciated that themethod of the present invention is not restricted to optical storage andaddressing systems. For example, the storage medium and addressingsystem may be a magnetically based system in which the information isstored magnetically within the memory-centers in the storage medium, andwherein I_(m) is the magnetic intensity within the pre-selected regionof the mth memory-center. In this case each memory-center comprises amagneto-sensitive constituent associated with each nano-particle whenthe storage medium is comprised of a periodic array of nanoparticles.The polymeric cores may be rigid polymeric cores such as, but notlimited to, latex spheres.

Thus in the broadest aspect the present invention provides a method ofreading binary information stored in a storage medium, comprising

providing a storage medium having n memory-centers each with a knownposition and the memory-centers having substantially the same physicaldimensions;

accessing the storage medium with an addressing system and measuring foreach memory-center a scalar signal intensity I_(m) emitted from apre-selected region which is centered on the known position of thememory-center; and

extracting the stored binary information by calculating bit values b_(n)for all memory-centers using an equation B=C⁻¹ I/I_(o), wherein I_(o) isa predetermined normalizing factor, I=(I₁, I₂, . . . , I_(n)) is anarray of the scalar intensities for all memory-centers, and B=(b₁, b₂, .. . , b_(n)) is an array of bit values, and C is a predeterminedcross-talk matrix of n² elements where each element represents across-talk between the pre-selected regions.

The value of each matrix element may be defined as a function of aspacing between memory-centers i and j given byC _(ij) =f(r′)=f(| r _(i) −r _(j)|)=f(R _(ij))where f(r′) is defined as a cross-talk function, and wherein thecross-talk matrix C is calculated by applying the cross-talk function toeach element of a matrix R that contains all inter-memory-centerspacings R_(ij)=r′=|r _(i)−r _(j)|.

The cross-talk function f(r′) may be derived from an intensitydistribution within a preselected region I₀(q _(m)),${f\left( r^{\prime} \right)} = {{\oint{{\mathbb{d}\underset{\_}{q}}{I_{0}\left( {\underset{\_}{q}}_{i} \right)}}}\bigcap{I_{0}\left( {\underset{\_}{q}}_{j} \right)}}$where q_(m) defines coordinates of the intensity distribution of thepreselected region of the mth memory-center.

A binary value for each memory-center is calculated from a correspondingbit value by a process wherein the n₁ highest bit values are assigned abinary value of ‘1’ and all others are assigned a binary value ‘0’ basedupon an equation relating the population of ‘1’ valued memory-centers,$n_{1} = {{\sum\limits_{j = 1}^{N}\quad\frac{I\quad j}{I_{0}}} = \frac{I_{N}^{total}}{I_{0}}}$

In all embodiments of the storage medium and addressing system, thestorage medium may be a 1-, 2- or 3-dimensional storage medium. Thestorage medium may be addressed in 1-, 2- or 3-dimensions using theaddressing system.

The storage medium may not necessarily be a nanocomposite based storagemedium and instead my be a homogeneous optical storage medium in whichthe memory-centers are “written-in” with pre-selected dimensions.

Similarly, the storage medium may be a homogeneous magnetic storagematerial.

The foregoing description of the preferred embodiments of the inventionhas been presented to illustrate the principles of the invention and notto limit the invention to the particular embodiment illustrated. It isintended that the scope of the invention be defined by all of theembodiments encompassed within the following claims and theirequivalents.

1. A method of reading binary information stored in a storage medium,comprising a) providing a storage medium having n memory-centers eachwith a known position and the memory-centers having substantially thesame physical dimensions; b) accessing said storage medium with anaddressing system and measuring for each memory-center a scalar signalintensity I_(m) emitted from a pre-selected region which is centered onthe known position of said memory-center; and c) extracting the storedbinary information by calculating bit values b_(n) for allmemory-centers using an equation B=C⁻¹ I/I_(o), wherein I_(o) is apredetermined normalizing factor, I=(I₁, I₂, . . . , I_(n)) is an arrayof said scalar intensities for all memory-centers, and B=(b₁, b₂, . . ., b_(n)) is an array of bit values, and C is a predetermined cross-talkmatrix of n² elements where each element represents a cross-talk betweensaid pre-selected regions and wherein the value of each matrix elementis defined as a function of a spacing between memory-centers i and jgiven byC _(ij) =f(r′)=f(| r _(i) −r _(j)|)=f(R _(ij)) where f(r′) is defined asa cross-talk function, and wherein said cross-talk matrix C iscalculated by applying said cross-talk function to each element of amatrix R that contains all inter-memory-center spacings R_(ij)=r′=|r_(i)−r _(j)|.
 2. The method according to claim 1 wherein a first row ofthe matrix R corresponds to the distances between the firstmemory-center and all other memory-centers and is calculated usinginteger combinations of a basis vector R _(1n)=A_(n) a+B_(n) b+C_(n) c,and wherein the jth row is calculated by transforming the origin fromthe first memory-center to the jth memory-center, |R_(jn)|=|R _(1n)−R_(1j)|.
 3. The method according to claim 1 wherein the cross-talkfunction f(r′) is derived from an intensity distribution within apre-selected region I₀(q _(m)),${f\left( r^{\prime} \right)} = {{\oint{{\mathbb{d}\underset{\_}{q}}{I_{0}\left( {\underset{\_}{q}}_{i} \right)}}}\bigcap{I_{0}\left( {\underset{\_}{q}}_{j} \right)}}$where q_(m) defines coordinates of the intensity distribution of thepre-selected region of the mth memory-center.
 4. The method according toclaim 1 wherein a binary value for each memory-center is calculated froma corresponding bit value by a process wherein the n₁ highest bit valuesare assigned a binary value of ‘1’ and all others are assigned a binaryvalue ‘0’ based upon an equation relating the population of ‘1’ valuedmemory-centers,$n_{1} = {{\sum\limits_{j = 1}^{N}\quad\frac{I\quad j}{I_{0}}} = {\frac{I_{N}^{total}}{I_{0}}.}}$5. The method according to claim 1 wherein said storage medium is a 1-,2- or 3-dimensional storage medium.
 6. The method according to claim 1wherein said storage medium is addressed in 1-, 2- or 3-dimensions. 7.The method according to claim 1 wherein the storage medium includes ahomogeneous optical storage material.
 8. A method of reading binaryinformation stored in a storage medium, comprising a) providing astorage medium having n memory-centers each with a known position andthe memory-centers having substantially the same physical dimensions; b)accessing said storage medium with an addressing system and measuringfor each memory-center a scalar signal intensity I_(m) emitted from apre-selected region which is centered on the known position of saidmemory-center and having an intensity distribution defined by an impulseresponse of the addressing system and an effective distribution of thesignal stored within the addressed memory-center; and c) extracting thestored binary information by calculating bit values b_(n) for allmemory-centers using an equation B=C⁻¹ I/I_(o), wherein I_(o) is apredetermined normalizing factor, I=(I₁, I₂, . . . , I_(n)) is an arrayof said scalar intensities for all memory-centers, and B=(b₁, b₂, . . ., b_(n)) is an array of bit values, and C is a predetermined cross-talkmatrix of n² elements where each element represents a cross-talk betweensaid pre-selected regions.
 9. The method according to claim 8 whereinthe intensity distribution within a pre-selected region I₀(q), iscalculated as the convolution of the impulse response with the effectivedistribution of the signal stored within the addressed memory-center,and wherein the value of each matrix element is defined as a function ofa spacing between memory-centers i and j given byC _(ij) =f(r′)=f(| r _(i) −r _(j)|)=f(R _(ij)) where f(r′) is defined asa cross-talk function, and wherein said cross-talk matrix C iscalculated by applying said cross-talk function to each element of amatrix R that contains all inter-memory-center spacings R_(ij)=r′=|r_(i)−r _(j)|.
 10. The method according to claim 9 wherein intensitydistribution is a spatial intensity distribution defined as,I ₀(x,y)=I _(i)(x,y)*S(x,y)=∫∫I _(i)(x,y)S(x′−x,y′−y)dx′dy′ where I_(i)is a spatial distribution of the impulse response and S is the effectivedistribution of the signal stored within a memory-center, and whereinthe cross-talk function f(r′) is derived from the spatial intensitydistribution within the pre-selected regions I₀(x,y),f(r^(′)) = 4 * ∫_(r/2)^(R)∫₀^(y(x))Io(x, y)𝕕y𝕕x where R is an effectiveradius of said spatial intensity distribution.
 11. The method accordingto claim 10 wherein the spatial intensity distribution measured withinthe pre-selected regions include discrete pixels I₀(x,y)=I⁰ _(x,y), andwherein the cross-talk function is${{f\left( r^{\prime} \right)} = {4*{\sum\limits_{r/2}^{R}{\sum\limits_{0}^{y{(x)}}I_{x,y}^{0}}}}},$where R is the effective radius of the spatial impulse response.
 12. Themethod according to claim 9 wherein the storage medium includes ahomogeneous optical storage material.
 13. The method according to claim8 wherein a binary value for each memory-center is calculated from acorresponding bit value by a process wherein the n₁ highest bit valuesare assigned a binary value of ‘1’ and all others are assigned a binaryvalue ‘0’ based upon an equation relating the population of ‘1’ valuedmemory-centers,$n_{1} = {{\sum\limits_{j = 1}^{N}\frac{I\quad j}{I_{0}}} = {\frac{I_{N}^{total}}{I_{0}}.}}$14. The method according to claim 13 wherein a first row of the matrix Rcorresponds to the distances between the first memory-center and allother memory-centers and is calculated using integer combinations of abasis vector R _(1n)=A_(n) a+B_(n) b+C_(n) c, and wherein the jth row iscalculated by transforming the origin from the first memory-center tothe jth memory-center, |R_(jn)|=|R _(1n)−R _(1j)|.
 15. The methodaccording to claim 8 wherein the information is stored optically withinthe memory-centers in the storage medium, and wherein I_(m) is the totaloptical intensity within the pre-selected region of the mthmemory-center.
 16. The method according to claim 8 wherein theinformation is stored magnetically within the memory-centers in thestorage medium, and wherein I_(m) is the magnetic intensity within thepre-selected region of the mth memory-center.
 17. The method accordingto claim 16 wherein the storage medium includes a periodic array ofnano-particles, and wherein each memory-center comprises amagneto-sensitive constituent associated with each nano-particle. 18.The method according to claim 17 wherein said periodic array ofnano-particles includes a polymer matrix comprising a three dimensionalarray of rigid polymeric cores embedded in a substantially transparentshell-forming polymer.
 19. The method according to claim 18 wherein saidrigid polymeric cores are latex spheres.
 20. The method according toclaim 16 wherein the storage medium includes a homogeneous magneticstorage material.
 21. The method according to claim 8 wherein thestorage medium includes a periodic array of nano-particles, and whereineach memory-center comprises a photosensitive constituent associatedwith each nano-particle.
 22. The method according to claim 21 whereinsaid photosensitive constituent includes chromophores.
 23. The methodaccording to claim 22 wherein said chromophores are fluorescentmolecules.
 24. The method according to claim 8 wherein said storagemedium is a 1-, 2- or 3-dimensional storage medium.
 25. The methodaccording to claim 8 wherein said storage medium is addressed in 1-, 2-or 3-dimensions.
 26. A method of reading binary information stored in anoptical storage medium, comprising a) providing an optical storagemedium having n memory-centers each with a known position and thememory-centers having substantially the same physical dimensions; b)accessing said optical storage medium with an optical addressing systemand measuring for each memory-center a total optical intensity I_(m)emitted from a pre-selected region which is centered on the knownposition of said memory-center and having an optical intensitydistribution within a single pre-selected region I₀(q) defined by apoint spread function of the optical addressing system and an intensitydistribution of the memory-center itself defined by an optical responseof a single memory-center as imaged through an idealized opticaladdressing system having an infinitely small point spread function; andc) extracting the stored binary information by calculating bit valuesb_(n) for all memory-centers using an equation B=C⁻¹ I/I_(o), whereinI_(o) is a predetermined normalizing factor, I=(I₁, I₂, . . . , I_(m), .. . , I_(n)) is an array of said scalar intensities for allmemory-centers, and B=(b₁, b₂, . . . , b_(n)) is an array of bit values,and C is a predetermined cross-talk matrix of n² elements where eachelement represents a cross-talk between said pre-selected regions. 27.The method according to claim 26 wherein the optical intensitydistribution within the single pre-selected region I₀(q), is calculatedas a convolution of the point spread function of the optical addressingsystem with the intensity distribution of the memory-center defined bythe optical response of the single memory-center as measured throughsaid idealized optical addressing system, and wherein the value of eachmatrix element is defined as a function of a spacing betweenmemory-centers i and j given byC _(ij) =f(r′)=f(| r _(i) −r _(j)|)=f(R _(ij)) where f(r′) is defined asa cross-talk function, and wherein said cross-talk matrix C iscalculated by applying said cross-talk function to each element of amatrix R that contains all inter-memory-center spacings R_(ij)=r′=|r_(i)−r _(j)|.
 28. The method according to claim 27 wherein thecross-talk function f(r′) is derived from an intensity distributionwithin the single pre-selected region I₀(q _(m)),${f\left( r^{\prime} \right)} = {\oint{{\mathbb{d}\underset{\_}{q}}{I_{0}\left( {\underset{\_}{q}}_{i} \right)}I\quad{I_{0}\left( {\underset{\_}{q}}_{j} \right)}}}$where q_(m) defines coordinates of the intensity distribution of thepre-selected region of the mth memory-center.
 29. The method accordingto claim 27 wherein the optical intensity distribution is a spatialintensity distribution defined as,I ₀(x,y)=PSF(x,y)*S(x,y)=∫∫I _(i)(x,y)S(x′−x,y′−y)dx′dy′ where PSF(x,y)is the point spread function of the optical addressing system and S(x,y)is said optical intensity distribution of the single memory-center asmeasured through said idealized optical addressing system, and whereinthe cross-talk function f(r′) is derived from the spatial intensitydistribution within the pre-selected regions I₀(x,y),f(r^(′)) = 4 * ∫_(r/2)^(R)∫₀^(y(x))Io(x, y)𝕕y𝕕x where R is an effectiveradius of the optical intensity distribution.
 30. The method accordingto claim 29 wherein the optical intensity distribution measuredoptically within the pre-selected regions includes discrete pixelsI₀(x,y)=I⁰ _(x,y), and wherein the cross-talk function is${{f\left( r^{\prime} \right)} = {4*{\sum\limits_{r/2}^{R}{\sum\limits_{0}^{y{(x)}}I_{x,y}^{0}}}}},$where R is the effective radius of the optical intensity distribution.31. The method according to claim 27 wherein a binary value for eachmemory-center is calculated from a corresponding bit value by a processwherein the n₁ highest bit values are assigned a binary value of ‘1’ andall others are assigned a binary value ‘0’ based upon an equationrelating the population of ‘1’ valued memory-centers given by,$n_{1} = {{\sum\limits_{j = 1}^{N}\frac{I\quad j}{I_{0}}} = {\frac{I_{N}^{total}}{I_{0}}.}}$32. The method according to claim 27 wherein a first row of the matrix Rcorresponds to the distances between the first memory-center and allother memory-centers and is calculated using integer combinations of abasis vector R _(1n)=A_(na+B) _(n) b+C_(n) c, and wherein the jth row iscalculated by transforming the origin from the first memory-center tothe jth memory-center, |R_(jn)|=|R _(1n)−R _(1j)|.
 33. The methodaccording to claim 27 wherein said storage medium is addressed in 1-, 2-or 3-dimensions.
 34. The method according to claim 27 wherein thestorage medium includes a periodic array of nano-particles, and whereineach memory-center comprises a photosensitive constituent associatedwith each nano-particle.
 35. The method according to claim 34 whereinsaid periodic array of nano-particles includes a polymer matrixcomprising a three dimensional array of rigid polymeric cores embeddedin a substantially transparent shell-forming polymer.
 36. The methodaccording to claim 35 wherein said rigid polymeric cores are latexspheres.
 37. The method according to claim 34 wherein saidphotosensitive constituent includes chromophores.
 38. The methodaccording to claim 37 wherein said chromophores are fluorescentmolecules.
 39. The method according to claim 27 wherein the storagemedium includes a homogeneous optical storage material.
 40. The methodaccording to claim 26 wherein said storage medium is a 1-, 2- or3-dimensional storage medium.